Sancho has been excluded from United's squads for both of their Premier League games this season, and Chelsea's interest in the winger gained traction earlier in the week.
The Red Devils have been open to selling the 24-year-old throughout the summer, even though Erik ten Hag welcomed him back into the squad and claimed that their dispute from last season had been resolved.
Juventus showed interest in signing Sancho on loan in recent days, but there is a sense within the Italian club that the 24-year-old prefers a move to Stamford Bridge.
As a result, they are now unlikely to pursue a deal for the United winger, but Chelsea seem to be making an effort to get a deal over the line late in the day.
Chelsea table improved loan offer for Sancho
According to Sky Sports, Chelsea have made an offer to Manchester United for Sancho, which is said to be a loan deal with an obligation to buy the player if certain thresholds are met.
Chelsea initially proposed including either Raheem Sterling or Ben Chilwell in a potential swap deal for the 24-year-old, but United declined the opportunity to sign either of the Blues players.
It is understood that United engaged in exploratory talks with the West Londoners regarding a move for Sterling, but the Sancho deal is now being pursued as a separate, standalone offer.
The Blues' loan offer for the England international is similar to that of Juventus but is believed to include a higher loan fee and cover a larger portion of his wages.
United would prefer to sell Sancho but have not ruled out the possibility of arranging another loan for the winger, who spent the second half of last season on loan at Borussia Dortmund.
Sancho has two years left on his contract at Old Trafford, with the club holding the option to extend it for an additional year if they choose.
Players who could depart Old Trafford before deadline
While United seem to have shut up shop in terms of new signings for the summer, there are still several players who could depart Old Trafford before the 11pm deadline.
Among those are Scott McTominay, who is reportedly set to make a switch to Serie A to join Napoli on a permanent basis for a reported fee of around £25.4m.
Victor Lindelof is now Manchester United's sixth-choice centre-back following the arrival of Leny Yoro and could move on today, though he is currently suffering from a toe injury which could put off potential suitors.
Christian Eriksen has not featured at all for Manchester United in the opening games of this season and has been linked with a move back to his former employers Ajax.
There could also be a few more loan deals for some of the younger players in the United squad, including the likes of Sonny Aljofree, Sam Mather and Sam Murray.